In this PhD. Thesis we focus on diffusion models. Diffusions are very attractive and widely applied in many scientific areas, since they provide a useful mathematical tool: the stochastic calculus. Let us think, for instance, to the Finance area. A large class of financial models use both diffusion processes and the stochastic calculus machinery, in order to price financial derivatives or to solve stochastic optimization problems. Thus convinced that diffusions are very important and useful for modeling natural and financial phenomena, we will focus our attention on their statistical analysis. In particular, the main goal of this Thesis will be the definition of a specific robust method, to make parametric inference for the drift and the diffusion coefficients of discretely observed diffusion processes.